Business analyses concerning products or other items are fundamental tasks for many manufacturers, suppliers, retailers, and other enterprises. Many business analyses are based on base sales volume. For example, demand forecasting, price-demand-behavior analysis, and promotional effectiveness analysis all rely on sound base sales volume measurement. Base sales volume (sometimes referred to as base volume in the remainder of this application) for consumer packed goods (CPG) is typically defined as the portion of the sales volume that would be expected without advertising or other promotional support. In many business analyses, base volume may be used as a de-causalized factor, such that a small difference in base volume may cause large deviations in the consequent analysis. Many business analyses are frustrated by such propagation of errors in base volume estimation.
In general, base volume is an unobserved component of actual sales volume (often referred to as actual volume in the remainder of this application), which is the observed or recorded sales volume. Ideally, one could determine true base volume through observation, the accuracy being limited only by the observational error. In practice, however, one can only observe the actual volume—the true base volume cannot be directly observed. It is not difficult to show that any estimate of the true base volume based on the observed actual volume and a Lyapunov error function (estimation criteria) will be biased. For example, the most common approach for determining promotional lifts based on estimated base volume generates incorrectly negatively signed lifts as much as thirty-five percent of the time; that is, determines a negative lift (decreased sales) when the lift should actually be positive (increased sales). In addition, conventional moving average approaches for estimating base volume depend on both the number of leads and/or lags involved and weights associated with the leads and/or lags. The complexity of the resulting space significantly impedes the ability to search for globally optimal solutions, making such approaches inferior.
Many businesses lack suitable approaches for measuring base sales volume, for example, for CPG in the presence of one or more promotional activities. These businesses are therefore unable to fully understand the various demand components for their products, which detracts from their ability to effectively plan and manage important business activities. Furthermore, establishing effective approaches to the complex problem of estimating base volume has become an increasingly important pursuit, from a theoretical perspective, in the academic community. As a result of any of the above or other factors, prior techniques for estimating base volume have been inadequate to meet the needs of many business and other users.